## 220 Reputation

17 years, 96 days
Kharkov
PhD in Numerical Optimization.

## Different values of numerical integratio...

Maple 2015

Dear friend,

Recently I noticed, that numerical integration returns different values for the same function.

For example the code

restart;
evalf(int((exp(x)*(4420*cos(4)*sin(4)-544*cos(4)^2+148147*exp(-1)-4225*cos(4)-215203)/(71825*exp(1)-71825*exp(-1))-exp(-x)*(4420*cos(4)*sin(4)-544*cos(4)^2+148147*exp(1)-4225*cos(4)-215203)/(71825*exp(1)-71825*exp(-1))+(32/4225)*cos(4*x)^2+(1/71825)*(4225+(2210*x-6630)*sin(4*x))*cos(4*x)+x^2+8434/4225)^2, x = 0 .. 1));

each time returns values

0.0005951015934
0.0005950850548
0.0005950974588
0.0005950960805
0.0005951297843 etc.

Maybe, evalf uses a stochastic algorithm for integration?

## Reading specified line of a text file...

Maple 2015

Dear friends.

I need a simple approach for reading a specified line of a text file.

FileTools[Text] module allows to count the lines. By sequential reading of lines it's possible to reach any position in the file. But for large file this takes a lot of time.

FileTools[Position] allows to set/get position in the file, but the position is counted in bytes.

Are there any workarounds for the problem or the use of Database Package is more preferable?

## Multiple vector plot...

Maple 2015

Maple function plot allows to build a linear plot for two vectors, when one vector contains X coordinates, another -- Y coordinates (similar to plot below):

Is it possible to build such a plot for several Y-vectors like this:

## Plots in one output cell...

Maple 18

Is it possible to organize output of plots in Mathematica-like manner

in one list (placed in one cell)?

In Maple I use tables for these purposes:

Maybe, does there exist a more elegant solution?

## Correct saving of dsolve' results ...

I try to save results of numeric integration of ODE, returned by dsolve. I address very simple equation and before saving all works as needed:

S1 := dsolve([diff(z(x), x\$2)+z(x) = -2, z(0)=0, z(1)=1], z(x), 'numeric', 'output' = listprocedure);

F1 := unapply(rhs(S1[2])(x), x); plot(F1, 0..1, thickness=3);

Next I save solution S1 by save operator:

save S1,  filename;

S1 saved and likely looks correctly:

S1 := [x = proc (x) local _res, _dat, _solnproc; option
:= Array(1..4, {1 = proc (outpoint) local X, Y, YP, yout, errproc, L, V, i; ........................................................

but

F1 := unapply(rhs(S1[2])(x), x);

returns an error:

Error, (in unknown) invalid input: the 1st argument to pointto is not a valid pointer handle

How to save solution correctly?

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